A Similarity Invariant and the Commutant of some Multiplication Operators on the Sobolev Disk Algebra. (2nd September 2012)

• Record Type: Journal Article
• Authors: Zhao, Ruifang
• Other Names: Schechtman Gideon Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2012(2012)
• Publication Date: 2012-09-02
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2012/378217
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : Let R ( 𝔻 ) be the algebra generated in Sobolev space W 22 ( 𝔻 ) by the rational functions with poles outside the unit disk 𝔻 ¯ . In this paper, we study the similarity invariant of the multiplication operators M g in ℒ ( R ( 𝔻 ) ), when g is univalent analytic on 𝔻 or M g is strongly irreducible. And the commutants of multiplication operators whose symbols are composite functions, univalent analytic functions, or entire functions are studied.